The interpolation of finite length sampled signals often result in savers distortion due to the leakage in spectrum caused by time domain truncation. In this paper a fast interpolation algorithm originated from the classical Whittaker Reconstruction is first derived. And basis transform is then introduced in extending Campbell Reconstruction to general finite length signals. Combining the above two measure presents a fast algorithm that effectively eliminate the defect of truncation. Analysis and tests shows that this new method can usually give satisfactory result.